Defect-induced photoluminescence of strontium titanate and its modulation by electrostatic gating
aa r X i v : . [ c ond - m a t . s t r- e l ] D ec Defect-Induced Photoluminescence of Strontium Titanate and its Modulation byElectrostatic Gating
Dushyant Kumar and R. C. Budhani*
Condensed Matter Low Dimensional Systems Laboratory,Department of Physics, Indian Institute of Technology, Kanpur 208016, India ∗ (Dated: December 18, 2015)The photoluminescence (PL) spectra of Ar + -ion irradiated single crystals of SrTiO (STO) ex-cited by 325 nm line of a He-Cd laser are compared with those of pristine crystals, epitaxial films andamorphous layers of STO at several temperatures down to 20 K. The 550 eV Ar + -beam irradiationactivates distinctly visible three PL peaks; blue ( ∼
430 nm), green ( ∼
550 nm), and infra-red ( ∼ ≈
100 K are discussed in relation with the antiferrodistortive structural phase tran-sition in SrTiO from cubic-to-tetragonal symmetry which makes it a direct bandgap semiconductor.The photoluminescence spectra are also tuned by electrostatic gate field in a field-effect transistorgeometry. At 20 K, we observed a maximum increase of ∼
20% in PL intensity under back gatingof SrTiO . I. INTRODUCTION
Strontium titanate (SrTiO ) is perhaps the mostwidely studied perovskite because of its unusual and tech-nologically important properties, which also make it apromising material for the oxide-based electronics. Atambient temperature SrTiO (STO) is a cubic crystal(Pm3m) with an indirect band gap of 3.27 eV. A cubic-to-tetragonal structural phase transition at ≈
105 K makesSTO a direct bandgap semiconductor and a precipitousgrowth of dielectric function follows below this temper-ature. High quality single crystals of STO have beenused as substrates for epitaxial growth of many othertransition metal oxides. It is also an ideal material forgate dielectric in field effect transistors (FET) due to itslarge dielectric constant.
The properties of STO can bevaried from insulating to semiconducting , metallic andeven superconducting at low temperatures on elec-tron doping. Recently, it has been demonstrated thatthe interfaces of STO with perovskite oxides like LaAlO and LaTiO can stabilize a two dimensional electron gas(2DEG) with mobilities as high as ∼ cm /V s . However, a 2DEG can also be formed on the surface ofbare STO either by electrostatic gating or by Ar + -ionirradiation. The later creates oxygen vacancies on thesurface of STO, which make it metallic.
Many groupshave studied this surface electron gas and have reportedits unique properties , which include a large ( ≈ , electrostatic con-trol of carrier concentration, persistent photoconductiv-ity and its control by electrostatic gating. In the context of optical properties, while the undopedstoichiometric single crystals of STO do not show any PLat room temperature, a broad greenish luminescence isseen near ≈
10 K. The intensity of this emission decreasesrapidly above 60 K and disappears all together beyond110 K.
The luminescence becomes pronounced whenoxygen vacancies are incorporated in STO.
Kan etal. have noted that bombardment with 300 eV Ar + - ionsinduces blue ( ∼
420 nm) PL in stoichiometric single crys- tals of STO at room temperature, which they attributeto emission from oxygen vacancies related defect states. However, a recent experiment of Sung et al. on 100 keVAr + -ion irradiated STO shows only a broad luminescencecentered at ∼
510 nm at room temperature. Since thenature of defects may change with ion energy, ion typeand their fluence, these results indicate much diverse na-ture of defect physics in this material. The PL emis-sion is generally derived from localized electronic stateswithin the forbidden gap created by atomic vacancies orimpurities.
The vacancies/defects present in Ar + -ionirradiated STO may not be of just single kind but in var-ious different forms leading to far more abundant defectstates. Indeed, the local density approximation (LDA)+ Hubbard U study carried out recently on oxygen de-ficient STO predicts that linear vacancy clusters resultin many localized in-gap states. This suggests the pos-sibility to activate several PL emissions simultaneouslyat room temperature in Ar + -ion irradiated STO. More-over, it is expected that the nature and abundance ofthe surface states can be tuned by electrostatic gatingto achieve multi-color optical devices. In view of theseinteresting predictions of the LDA+U theory, it is desir-able to further explore the photoluminescence of Ar + -ionirradiated STO and its other forms over a broad rangeof temperatures to cover the direct to indirect opticalgap regimes. Moreover, since the PL is a very sensitiveand selective probe of defect/impurity states, studies ofluminescence would improve our understanding of thepersistent photoconductivity reported earlier in Ar + -ionirradiated STO. Here we present a detailed study of photoluminescenceof oxygen-deficient SrTiO created by Ar + -ion irradia-tion over a broad range of temperature and compare itwith our measurements of the PL in pristine crystals,epitaxial films and amorphous layers of the same mate-rial. While we did not observe any luminescence from thepristine STO at ambient temperature, the ion irradiationled to a multi-frequency emission. However, below ≃ ≈
500 nm. It is also shown that the photolu-minescence spectrum can be modulated by electrostaticgating at low temperatures ( <
20 K) which may be po-tentially important for applications.
II. EXPERIMENTAL DETAILS
The stoichiometric single crystals of SrTiO used inthis study were acquired from Crystal GmbH Germany.The (001) surface of these 0.5 mm thick and opticallypolished plates was irradiated at room temperature byAr + - ions with a cumulative doses of ∼ × , 4.2 × and 6 × ions/cm . The typical accelerationvoltage and ion current used in these experiments, carriedout with a Kauffman type ion source operated at ∼ × − mbar Ar pressure, were 550 V and 1.5 mA/cm ,respectively. The irradiated surface of STO is metallicdown to the lowest temperature ( ≈
10 K) where the sheetresistance and carrier mobility are ∼ (cid:3) and ∼ × cm /Vs respectively. Further details of the Ar + -ionirradiation experiments and measurements of electronictransport in irradiated samples are given in our earlierarticle. The photoluminescence spectra were excitedwith the 325 nm line of a He-Cd laser, and measuredusing Jobin Yvon Triax-320 spectrometer. For measure-ments of the temperature dependence of PL spectra, thesamples were mounted in a close cycle helium cryostathaving a quartz window for optical access. The PL re-sponse was also modulated electrostatically by gating theirradiated surface in a back gate configuration.
III. RESULTS
In Fig. 1(a), we show the room temperature photolu-minescence spectrum of the (001) surface of Ar + -ion ir-radiated SrTiO . In the same figure we have also shownthe feature less PL response of a non-irradiated sample.The richness of the spectrum in the former case is a tes-timony of enhanced optical activity as a result of ionirradiation. The spectrum shows three distinct emissionpeaks centered at ∼
430 nm, ∼
550 nm and ∼
820 nm,which on the energy scale correspond to ∼ ∼ ∼ ∼
430 nm) observed in this study is essentially the sameas that reported by Kan et al. in their 300 eV Ar + -ionirradiated STO. But these authors did not observe thetwo additional peaks seen here which result in a multi-colored photoluminescence at room temperature in these550 eV Ar + -ion irradiated STO crystals.Since heavy ion irradiation can cause amorphizationof the target surface, we have also studied the effects ofpost irradiation etching of STO on its photoluminescencecharacteristics. For this purpose two STO samples 3 × were irradiated together to avoid any discrep-ancy. After irradiation, one of the samples was chemi-
300 450 600 750 9000.00.10.20.3 P L I n t. ( x a . u . ) non-irradiatedIrradiated (nm)
30 sec. HF etching after irradiation (a)
T = 300 K
300 450 600 750 90001020304050 (nm)
HF etching 0 sec 30 sec P L I n t. ( x a . u . ) (b) T = 20 K
368 391 41401 I n t. ( x a r b . ) (nm) FIG. 1. (Color online) Multi-color PL spectra of Ar + -ion ir-radiated STO and the effect of hydrofluoric (HF) acid etching(a) at 300 K and (b) at 20 K. The HF treatment of irradiatedSTO increases the PL intensity at 300 K by a factor of two.For reference, the PL of non-irradiated stoichiometric STO isalso shown in Fig. 1(a). The 390 nm peak at 20 K is zoomedin the inset of panel (b). cally etched in HF solution (NH F : DI water : HF =18.54 gm : 50 ml : 3.75 ml) for 30 seconds. For com-parison, the room temperature PL spectra of the etchedsample is also plotted in Fig. 1(a). It is observed thatthe HF etching increases the integrated PL peak inten-sity by a factor of two keeping the position and shapeof the peaks intact. The ion bombardment would cre-ate a large number of nanograins on the surface of theSTO. The SrO being very sensitive to HF attack, theetching process is likely to increase the amount of oxygen-vacancy defects by dissolving the SrO on the lateral sidesof these nanograins thus raising the conduction bandcarrier density and hence the PL intensity.Figure 2 illustrates the changes in PL spectra of theirradiated and etched samples at various temperaturesfrom 300 K down to 20 K. From panel (a), it can be seenthat the intensity of all the PL peaks increases graduallyon decreasing the temperature down to ∼
100 K. A slight
300 450 600 750 900 300 450 600 750 900 (nm)
360 390 420 4500.00.20.40.6
390 nm20 K (b)(a) (c)
300 K
20 K40 K60 K80 K100 K150 K200 K250 K P L I n t en s i t y (nm)
300 K n m P L I n t en s i t y
20 K40 K60 K80 K100 K150 K200 K250 K (nm)
300 K P L I n t. ( x a . u . ) FIG. 2. (Color online) PL spectra of Ar + -ion irradiated STOand non-irradiated (bare) STO in the temperature range of300 K to 20 K. Panel (a) shows the temperature dependenceemission spectra of Ar + -ion irradiated STO. For clarity, thespectra along with their deconvolution fit are shifted and theintensity of PL spectra at 20 K, 40 K and 60 K are reduced byfactor of 13, 10 and 3. These spectra are put together in panel(b) and zoomed in the vicinity of 390 nm peak emphasizing itsappearance below ∼
60 K. The similar measurements carriedout for bare STO are shown in panel (c) for comparison. Thespectra at 20 K and 40 K are reduced by factor of 12 and 9. shift in the position of the blue peak towards higher wave-length can also be noticed on cooling. On further decreas-ing the temperature from 100 K down to 60 K, the greenluminescence intensity increases dramatically, whereas,the blue luminescence appears to merge under the nowmuch broader emission with its peak at green. A closerexamination of these spectra further reveals the presenceof another emission peaked at ∼
390 nm [marked by anarrow in Fig 2(a) and Fig. 2(b)] whose intensity increaseson lowering the temperature. On reaching 20 K, an in-tense broad luminescence ranging from ∼
370 nm to ∼ ∼
390 nm isclearly visible in the figure [panel (a) and (b)]. Note thatthe later is not observed in stoichiometric non-irradiatedSTO [panel (c)]. The PL spectrum of un-etched (onlyirradiated) STO has also been collected at 20 K. Thespectrum is shown in Fig. 1(b) along with that of theetched irradiated STO. One can see that there is no ef-fect of etching on the greenish broad band luminescence,however, as clear from the inset of Fig. 1(b), it increases the 390 nm PL peak intensity by a factor of two.
300 400 500 600 700 800 9000.00.10.20.3
Amorphous thin filmEpitaxialthin film Ar + - irradiated STO P L I n t. ( x a . u . ) (nm) FIG. 3. (Color online) Photoluminescence profile of epitaxialoxygen deficient thin film and amorphous film of SrTiO atroom temperature. For comparison, the PL spectra of Ar + -irradiated STO is also shown. Note that the amorphous filmshows a broad featureless emission profile whereas the PLspectra of oxygen deficient film behave similar to that of Ar + -irradiated STO. We now turn our attention to the possible sources ofthe rich spectrum, whether it is oxygen deficient layeror the top amorphous layer. Towards this end, we haveexamined the PL properties of oxygen deficient epitax-ial thin films as well as amorphous films of STO. These100 nm thick films were grown on STO (001) substratesby pulsed laser ablation of a bulk target of SrTiO . Theoxygen deficient film was deposited under reduced oxygenenvironment (6.3 × − mbar) at 800 C substrate tem-perature. The epitaxial growth was confirmed by X-raydiffraction. This film showed a metallic behaviour downto 10 K coming from oxygen vacancy induced mobile elec-trons in the system as reported earlier by Perez-Casero et al. To grow the amorphous film, the deposition wascarried out at room temperature under 1 × − mbarof oxygen. Two samples of each type were prepared.Both of them showed similar PL results. The room tem-perature PL spectra of these films are shown in Fig.3 along with those of the Ar + -irradiated STO crystal.The amorphous film displays a broad featureless lumi-nescence ranging from 350 nm to 950 nm, which is in ac-cordance with the reported photoluminescence of amor-phous SrTiO . This emission profile clearly does notmatch with the luminescence of Ar + -irradiated STO.However, the emission behaviour of the oxygen deficientepitaxial film is close to that of the Ar + -irradiated STO,which suggests that the photoluminescence in the lateris mainly originating from the oxygen deficient layer.A unique feature of the present study is the modulationof the PL spectra with an electrostatic gate field as shownin Fig. 4(a) under a gate voltage varying from -150 V to+150 V at 20 K. These voltages translate into an electric -150 -75 0 75 1500.20.35060
300 450 600 750 9000.00.10.20.3 T = 300 K (b) V g (V) 0 +10 +30 +50 +100 +150 -10 -30 -50 -100 -150 P L I n t. ( x a . u . ) (a) T = 20 K
300 K
20 K P L I n t. ( x a . u . ) V g (V) V g (V) P L I n t. ( x a . u . ) (nm) FIG. 4. (Color online) PL modulation by electrostatic gatefield varying from -150 V to +150 V (a) at 20 K and (b) at 300K. The changes in broad green peak intensity as a functionof gate field are shown in the inset of panel (a). At 20 K, thegate field increases the peak-intensity where as there are nonoticeable changes at 300 K. field of -3 kV/cm to +3 kV/cm. The entire sweep of gatefield from zero to positive to negative and then back tozero took around ∼ IV. DISCUSSION
The broad spectrum stretching from ∼
380 nm to ∼
300 450 600 750 9000.00.10.20.3 n m n m n m n m n m P L I n t. ( x a . u . ) (nm) FIG. 5. (Color online) Deconvolution of PL spectra observedat room temperature. It reveals the presence of two morepeaks along with three peaks, which are distinctly visible inthe spectra. Multiple frequencies are marked by dashed lines.Cumulative fit is also drawn.TABLE I. The percentage area of each decomposed PL peakat 300 K.
Violet Blue Green Red Infra-red407 nm 435 nm 536 nm 631 nm 818 nm3% 15% 47% 30% 7%A similar analysis has been done for all the spectracollected in the temperature range of 20 K to 300 K. Thecumulative fits are drawn in Fig. 2(a). The peak po-sitions, their full width at half maximum (FWHM) andintensity derived from the deconvolution procedure areplotted in Fig. 6 as a function of temperature. Theintensity of all the peaks increases gradually on loweringthe temperature from 300 K to 100 K. This trend acceler-ates on further decreasing the temperature below ≈ ≈
100 K. From 300K to ≈
100 K, the blue and red peaks shift gently towardsgreen with no noticeable shift of the IR and violet peakpositions. However, in low-T region (below ≈
100 K), theresponse is remarkably different. At 60 K, the diversenature of luminescence is no more visible. There is onlya broad emission profile peaked at the position of thegreen line. It seems that all other peaks are merged un-der this broad and intense luminescence. Moreover, theintensity of this green signal increases sharply on low-ering the temperature. In the low T-region, a similarT-dependence has been reported for the greenish lumi-
50 100 150 200 250 300400500600700800 (b) P L I n t. ( x a . u . ) (a) F W H M ( n m ) T (K) P ea k P o s i t i on ( n m ) T (K)
390 407 435 536 631 818
Bare STO P L I n t. ba r e S T O ( x a . u . ) FIG. 6. (Color online) Temperature dependence of the char-acteristic features of the multiple peaks; (a) intensity, (b) peakposition, and the inset of (a) shows the FWHM. These fea-tures were extracted from the deconvolution of the PL spec-tra collected at several temperatures between 300 K to 20 K.Drastic changes in all of three can be seen around .
100 K.For comparison, the intensity of greenish luminescence of bareSTO is also plotted in panel (a). Lines are guide to the eye. nescence observed in undoped-stoichiometric STO.
We have also recorded the PL spectra of stoichiomet-ric non-irradiated STO (001) substrate throughout thetemperature range of 300 K to 20 K. The results areshown in panel (c) of Fig. 2. At 20 K, one can see anintense broad emission peaked at 540 nm, whose inten-sity decreases rapidly as the temperature is raised upto100 K, and becomes negligibly small at 150 K with nodetectable signal beyond 200 K. The PL spectra of non-irradiated STO at 20 K resembles well with that of theirradiated sample [Fig. 2(a)] except that the latter showsan extra peak in the vicinity of 390 nm. Moreover, theT-dependence of the green peak intensity of the irradi-ated sample in low T-region agrees well with that of thenon-irradiated STO [panel (a) of Fig. 6]. This compara-tive study suggests that below ≈
100 K the luminescenceof the non-irradiated part of STO underneath the dis-ordered region created by Ar + -ion irradiation dominatesover the emission signal coming from the oxygen deficientlayer in the ion affected region. Note that all of the PLproperties (peak position, line width and PL intensity) change abruptly below around ≈
100 K, the temperaturewhere SrTiO crystal undergoes a structural phase tran-sition from cubic-to-tetragonal.The multicolored PL seen in these experiments is con-sistent with the predictions of LDA+U calculations ofCuong et al. on oxygen deficient STO, where they haveshown that a single oxygen vacancy can create a shallowlevel just below ( ∼ ≈
390 nm.Incorporation of vacancy-vacancy interactions in the cal-culation yields oxygen vacancy clusters which induce lo-calized electronic levels ranging in energy from 0.3 eV to1.14 eV in the forbidden gap with respect to the con-duction band edge. Defect clusters can also result frombinding of oxygen and strontium vacancies. The acceler-ated Ar + -ions, while penetrating into the STO lose theirenergy resulting in an oxygen-deficient layer along withan amorphous layer on the top. We believe that theion irradiation is creating disorder in the material lead-ing to several different kinds of oxygen-vacancy clusterswhich induce many in-gap localized states. The recombi-nation of electrons trapped in these levels to the valenceband holes can lead to multi-frequency emission at roomtemperature.At this point it is worth commenting on why the pris-tine STO crystal shows an onset of photoluminescence at ∼
100 K which becomes quit pronounced around ≃
20 K.It is well known that cubic (Pm3m) SrTiO undergoesan antiferrodistortive ( O h → D h ) structural phase tran-sition (AFD-PT) to a tetragonal symmetry (I4/mcm) inthe vicinity of 105 K. In the cubic STO, the top of thevalence band is located at the R-point in the first Bril-louin zone where as the lowest conduction band bottomlies at the Γ-point making this transition indirect. TheAFD-PT results in merging of the R and Γ-points of theBrillouin zone of the cubic structure into the Γ-point oftetragonal phase, thereby transforming the lowest in en-ergy, indirect phonon-assisted R → Γ optical transitioninto the direct Γ → Γ transition.
We believe thatthis opening of the direct gap results in enhanced PLintensity in the pristine STO below 100 K.Now we discuss the possible origin of the increase inPL intensity as seen on applying a gate field. A voltage(positive/negative) on the gate induces onto the sample acharge (negative/positive), which, in the absence of sur-face states, distributes throughout a space charge region λ either in gap states or in the bands. Using Barbe the-ory of field effect , the induced space charge (Q sc ) perunit area in the semiconductor can be expressed as | Q sc | = n ǫǫ kTeλ o y s where ǫ is the dielectric constant of the material, ǫ is thepermittivity of free space, k is the Boltzmann constantand y s is the dimensionless energy at the surface. How-ever, in the presence of surface states/trapping centers inthe material, most of the induced charge falls into thesestates. The charge (Q ss ) residing in surface states canbe written as | Q ss | = ekT ( N FAS + N FDS ) y s where N FAS and N FDS are the number of acceptor type anddonor type surface states per unit area per unit energyat the Fermi level, respectively.In our case, the ion irradiation process is likely to cre-ate a large number of defects and thus midgap energystates. These states are plausible to be hole as well aselectron trap levels forming non-radiative recombinationsites which lower the intrinsic PL of STO in the directband gap state. These positive and negative recombi-nation centers can efficiently be deactivated by the varia-tion of relative position of the Fermi level using negativeand positive gate fields respectively . We expect thefilling of electron trap states while the gate field is swungpositive and the passivation of hole trap states when thegate field is swung negative. Therefore, the gate field re-gardless of its polarity will ensure the reduction of non-radiative recombination and hence the increase in PL in-tensity. On the other hand, at 300 K, where the gatefield due to low dielectric function is not that effective,it can only partially passivate these centers and hence nosignificant modulation of PL intensity is seen.
V. CONCLUSIONS
In summary, we have shown that the 550 eV Ar + -ionsirradiation induces a multi-color photoluminescence in stoichiometric single crystals of SrTiO (001) at roomtemperature, where no PL signal is seen in the pristinestate. The PL spectra of oxygen deficient and amor-phous thin films of SrTiO suggest that this multi-coloremission originates from oxygen deficient layers of the ir-radiated crystal. The luminescence intensity is enhancedfurther when the ion induced amorphous layer on surfaceof the STO is removed by etching. On cooling from 300K to 100 K, the luminescence intensity increases witha noticeable shift of the blue and red peaks toward themiddle of the spectrum. The diverse nature of PL dis-appeared below 80 K with a drastic increase in greenluminescence. At 20 K, a modulation of PL spectra wasachieved through the passivation of surface states by elec-trostatic back gating of the STO. ACKNOWLEDGMENTS
The authors thank A. Rastogi for initial help whiledoing photoluminescence measurements. D.K. would liketo acknowledge Indian Institute of Technology Kanpurfor partial financial support. R.C.B. acknowledges J. C.Bose National Fellowship of the Department of Scienceand Technology, Government of India. ∗ [email protected] C. Cen, S. Thiel, J. Mannhart, and J. Levy, Science ,1026 (2009). M. Kawasaki, K. Takahashi, T. Maeda, R. Tsuchiya,M. Shinohara, O. Ishiyama, T. Yonezawa, M. Yoshimoto,and H. Koinuma, Science , 1540 (1994). G. Koster, G. Rijnders, D. H. A. Blank, and H. Rogalla,Physica C: Superconductivity , 215 (2000). D. Newns, J. Misewich, C. Tsuei, A. Gupta, B. Scott, andA. Schrott, Applied Physics Letters , 780 (1998). H. Nakamura, H. Takagi, H. Inoue, Y. Takahashi,T. Hasegawa, and Y. Tokura, Applied physics letters ,133504 (2006). A. Rastogi, A. K. Kushwaha, T. Shiyani, A. Gangawar,and R. C. Budhani, Advanced Materials , 4448 (2010). O. N. Tufte and P. W. Chapman,Phys. Rev. , 796 (1967), URL http://link.aps.org/doi/10.1103/PhysRev.155.796 . H. P. R. Frederikse, W. R. Thurber, and W. R.Hosler, Phys. Rev. , A442 (1964), URL http://link.aps.org/doi/10.1103/PhysRev.134.A442 . J. F. Schooley, W. R. Hosler, and M. L. Co-hen, Phys. Rev. Lett. , 474 (1964), URL http://link.aps.org/doi/10.1103/PhysRevLett.12.474 . C. Koonce, M. L. Cohen, J. Schooley, W. Hosler, andE. Pfeiffer, Physical Review , 380 (1967). A. Ohtomo and H. Y. Hwang, Nature , 423 (2004). A. Rastogi, J. J. Pulikkotil, S. Auluck, Z. Hossain, andR. C. Budhani, Physical Review B , 075127 (2012). W. Meevasana, P. King, R. He, S. Mo, M. Hashimoto,A. Tamai, P. Songsiriritthigul, F. Baumberger, andZ. Shen, Nature Materials , 114 (2011). D. W. Reagor and V. Y. Butko, Nature Materials , 593(2005). D. Kan, T. Terashima, R. Kanda, A. Masuno, K. Tanaka,S. Chu, H. Kan, A. Ishizumi, Y. Kanemitsu, Y. Shi-makawa, et al., Nature Materials , 816 (2005). A. Gentils, O. Copie, G. Herranz, F. Fortuna, M. Bibes,K. Bouzehouane, E. Jacquet, C. Carr´et´ero, M. Basleti´c,E. Tafra, et al., Phys. Rev. B , 144109 (2010), URL http://link.aps.org/doi/10.1103/PhysRevB.81.144109 . F. Y. Bruno, J. Tornos, M. G. del Olmo, G. S. Santolino,N. M. Nemes, M. Garcia-Hernandez, B. Mendez, J. Pi-queras, G. Antorrena, L. Morell´on, et al., Physical ReviewB , 245120 (2011). D. Kumar, Z. Hossain, and R. C. Bud-hani, Phys. Rev. B , 205117 (2015), URL http://link.aps.org/doi/10.1103/PhysRevB.91.205117 . L. Grabner, Phys. Rev. , 1315 (1969), URL http://link.aps.org/doi/10.1103/PhysRev.177.1315 . Y. Sihvonen, Journal of Applied Physics , 4431 (1967). T. Feng, Phys. Rev. B , 627 (1982), URL http://link.aps.org/doi/10.1103/PhysRevB.25.627 . R. Leonelli and J. L. Brebner, Phys.Rev. B , 8649 (1986), URL http://link.aps.org/doi/10.1103/PhysRevB.33.8649 . K. D. Sung, R. Kumar, A. P. Singh, C. S. Kim,K. J. Yee, and J. H. Jung, Physica B: CondensedMatter , 2581 (2010), ISSN 0921-4526, URL . J. Rho, S. Jang, Y. D. Ko, S. Kang, D.-W. Kim,J.-S. Chung, M. Kim, M. Han, and E. Choi, Ap-plied Physics Letters , 241906 (2009), URL http://scitation.aip.org/content/aip/journal/apl/95/24/10.1063/1.3275707 . J. Rho, J. Kim, S. Shin, J. Kwon, M. Kim,J. Song, and E. Choi, Journal of Lumines-cence , 1784 (2010), ISSN 0022-2313, URL . K. Szot and W. Speier, Phys. Rev. B , 5909 (1999), URL http://link.aps.org/doi/10.1103/PhysRevB.60.5909 . D. D. Cuong, B. Lee, K. M. Choi, H.-S. Ahn, S. Han,and J. Lee, Phys. Rev. Lett. , 115503 (2007), URL http://link.aps.org/doi/10.1103/PhysRevLett.98.115503 . Z.-h. Li, H.-t. Sun, Z.-q. Xie, Y.-y. Zhao, and M. Lu, Nan-otechnology , 165703 (2007). R. Perez-Casero, J. Perriere, A. Gutierrez-Llorente,D. D´efourneau, E. Millon, W. Seiler, and L. Soriano, Phys-ical Review B , 165317 (2007). L. Soledade, E. Longo, E. Leite, F. Pontes, F. Lanciotti Jr,C. Campos, P. Pizani, and J. A. Varela, Applied PhysicsA , 629 (2002). C. Pinheiro, E. Longo, E. Leite, F. Pontes, R. Magnani,J. A. Varela, P. Pizanni, T. Boschi, and F. Lanciotti, Ap-plied Physics A , 81 (2003). E. Orhan, F. M. Pontes, M. A. Santos, E. R. Leite, A. Bel-tran, J. Andres, T. M. Boschi, P. S. Pizani, J. A. Varela,C. A. Taft, et al., The Journal of Physical Chemistry B , 9221 (2004). G. Shirane and Y. Yamada, Physical Review , 858(1969). E. Heifets, E. Kotomin, and V. A. Trepakov, Journal ofPhysics: Condensed Matter , 4845 (2006). P. Fleury, J. Scott, and J. Worlock, Physical Review Let-ters , 16 (1968). L. Mattheiss, Physical Review B , 4740 (1972). D. Barbe, Journal of Vacuum Science & Technology , 102(1971). M. S. Kang, J. Lee, D. J. Norris, and C. D. Frisbie, Nanoletters , 3848 (2009). C. Galland, Y. Ghosh, A. Steinbr¨uck, M. Sykora, J. A.Hollingsworth, V. I. Klimov, and H. Htoon, Nature ,203 (2011). Z. Li, S.-W. Chang, C.-C. Chen, and S. B. Cronin, NanoResearch , 973 (2014). J. Schornbaum, Y. Zakharko, M. Held, S. Thiemann,F. Gannott, and J. Zaumseil, Nano letters15